A school room is be built to accommodate 70 children so as to allow 2.2 m² of floor and 11 m³ of space for each child. If the room be 14 metres long, what must be its breadth and height ?

Solution(By Examveda Team)

Let the breadth and height of the room be b and h metres respectively.
Then,
Area of the floor $$ = \left( {14b} \right)\,{m^2}$$
$$\eqalign{ & \therefore 14b = 2.2 \times 70 \cr & \Rightarrow b = \frac{{2.2 \times 70}}{{14}} \cr & \Rightarrow b = 11 \cr} $$
Volume of the room :
$$\eqalign{ & = \left( {14 \times 11 \times h} \right){m^3} \cr & = \left( {154h} \right){m^3} \cr} $$

$$\eqalign{ & \therefore 154h = 11 \times 70 \cr & \Rightarrow h = \frac{{11 \times 70}}{{154}} \cr & \Rightarrow h = 5 \cr} $$